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Important situations in circular motion

Explore the concepts of centripetal force, acceleration, and gravitational force in circular motion. Learn about the factors affecting centripetal acceleration and the relationship between force and motion. Discover the law of universal gravitation and its implications for orbiting objects.

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Important situations in circular motion

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  1. Important situations in circular motion

  2. When accelerating, the feeling you have is opposite the acceleration This is why it feels like there is centrifugal acceleration when it’s really centripetal acceleration.

  3. Centripetal force is the general name given to the inward force The centripetal force IS THE Tension The centripetal force IS THE Friction The centripetal force IS THE Force of Gravity

  4. Notice the v and a are at right angles This is always true for uniform circular motion

  5. Newton’s first law dictates that the object will remain in straight line motion until a force cause turning

  6. This is the view from above for a board with a ball on it with and without a wall • As the cart turns, what happens to the ball? A force toward the center is necessary to cause turning.

  7. How much acceleration? • As you may have seen in the lab, centripetal acceleration depends on two factors: • The speed of the object (v) • The radius of the circular motion (r) • The magnitude of centripetal acceleration can be determined by the equation: ac = v2/r

  8. Other important measurements • Period (T): The time it takes for one complete rotation (measured in seconds) • Frequency (f): How many complete rotations happen per second (measured in Hertz; 1 Hz = 1 rotation per second) • We could also calculate ac using period or frequency (however, we won’t in this class)

  9. Free Body for anything circling vertically • Like a bucket of water • Both forces are down at the top • So doesn’t that mean the water will surely fall out? • Nope, inertia keeps the water moving in a straight line • The combined (net) forces are causing centripetal acceleration – making it turn • Acceleration is not the same as motion! (recall braking car – a is backwards but car moves forward)

  10. As the coaster goes around the loop the force for turning, the track, must be into the center of the loop. • What is the force from the track? • The normal force!! • At the top of the loop what direction is the normal force? • Down • Both gravity and the normal are directed downward

  11. Any time there is turning There must be an unbalanced net force causing an acceleration.

  12. Remember Newton’s 2nd Law!! F = ma For centripetal force, Fnet = mac

  13. Orbiting We know orbiting satellites have centripetal force What is the centripetal force here? Force of gravity Is gravity here Fg=mg=m*9.8 m/s2? NO! Why not? Too far from Earth for g=9.8m/s2 Is g = 0?

  14. NO! g≠0 ever! • You are in free fall, your “weightlessness” is due to lack of a normal force • Your inertia moves you tangent to the orbital path, but the gravity pulls you in • So how do you calculate the Fg?

  15. Law of Universal Gravitation Legend has it that Newton thought “an apple falls to the Earth because of the force of gravity. At what distance does the force stop pulling? Does the force of gravity pull on the moon?” Eventually he realized that there must be a gravitational force between every pair of objects The amount of force depended on the masses of the objects and the distance between them

  16. Law of Universal Gravitation

  17. For an orbiting object • F=ma • F= Fg = ma gravity is the only force • Fg = Gm1m2/r2 = ma • Gm1m2/r2 = ma = mv2/r • Same r’s so one cancels • One m is the mass of the object; it cancels • So all you need is the radius to find the velocity! • Gm1mearth/r2 = mv2/r so Gm2/r = v2

  18. Try some multiple choice at • www.wiley.com/college/cutnell general site • Specific to Ch. 5 self assessment http://www3.interscience.wiley.com:8100/legacy/college/cutnell/0471151831/sat/media/html/sat_c05/sat_c05.htm

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